一类微分方程反问题解的存在唯一性

对在等离子体和一维波动方程中出现的具有初始分布数据的一类双曲微分方程反问题，用压缩映像原理给出了解的存在唯一性。     

勒让德方程的广义格林函数

讨论非齐次微分方程奇边值问题的有效方法是格林函数法,而构造格林函数并非易事.本文对物理学的多极场展开中遇到的非齐次勒让德方程,在特征值λ=2的情况下,构造了广义格林函数,并给出了非齐次勒让德方程解的表达式.     

模态研究的数学分析与有限元分析的探讨

简单的结构可通过数学方法获得比较准确的模态结果,较复杂的结构很难用数学方法直接进行分析,需要将模型简化,不合理的简化会导致分析结果的错误,使用有限元软件分析可以获得比较理想的结果。划分网格是有限元分析的关键一步,文中以大拉杆为例,进行了数学计算、有限元软件ANSYS与ADINA模态分析,通过对比模态结果,对这两款不同有限元分析软件的计算特点进行了总结,得出并不是网格密度越密计算精度越高的结论。     

潜艇的三维厚边界层研究

建立了三维湍流边界层及尾流的动量积分方程,通过算例将计算结果与Gadd的结果进行比较和分析,验证了该方法的可靠性.在潜艇的粘性边界层计算过程中,应用了在势流理论基础上建立起来的艇体表面流线坐标系,对潜艇周围的三维厚边界层进行研究,得到了潜艇边界层及尾流的特征参数,给出了附体(围壳和尾翼)对特征参数的影响.在考虑排挤影响后,艇体采用等价源方法而尾流采用等价假想体法,通过势流计算得到潜艇表面的压力分布.     

RANS simulation of a container ship using a single-phase level-set method with overset grids and the prognosis for extension to a self-propulsion simulator

Steady flow simulations for the Korean Research Institute for Ships and Ocean Engineering (KRISO) container ship (KCS) were performed for towing and self-propulsion. The main focus in the present article is on the evaluation of computational fluid dynamics (CFD) as a tool for hull form design along with application of state-of-the-art technology in the flow simulations. Two Reynolds-averaged Navier-Stokes (RANS) equation solvers were employed, namely CFDShip-Iowa version 4 and Flowpack version 2004e, for the towing and self-propulsion cases, respectively. The new features of CFDShip-Iowa version 4 include a single-phase level-set method to model the free surface and an overset gridding capability to increase resolution in the flow and wave fields. The new features of Flowpack version 2004e are related to a self-propulsion scheme in which the RANS solver is coupled with a propeller performance program based on the infinitely bladed propeller theory. The present work is based on a close interaction between IIHR-Hydroscience and Engineering of the University of Iowa and Osaka Prefecture University. In the following article, overviews are given of the present numerical methods and results are presented and discussed for the KCS in towing and self-propulsion modes, including comparison with available experimental fluid dynamics (EFD) data. Additional evaluation is provided through discussion of the recent CFD Workshop Tokyo 2005, where both methods appeared to yield very promising results.     

一类双曲方程解的存在唯一性

对在等离子体和一维波动方程中出现的具体有初始分布数据的一类双曲微分方程正问题，将其化成第二类Volterra积分方程后，用压缩映像原理给出了解的存在唯一性。     

NSPMF-EB耦合模型及其在近岸波浪计算中的应用

提出通过耦合透水介质的流体运动方程(NSPMF模型)和改良Boussinesq方程(EB模型)来描述近岸水波现象的数学模型。NSPMF模型的优越性在于它能描述波浪破碎、越浪以及波浪和各种结构物(包括透水性结构物)之间的相互作用等伴随着复杂流动结构的局部波动现象;EB模型则可用于求解广阔海域内非线性不规则波浪的运动和变形过程。耦合模型兼有二者的优势,具有广阔的应用前景。验证计算的结果表明本文建议的耦合方法是有效的。     

The evaluation of high occupancy vehicle lanes on sun yat‐sen freeway in Taiwan

This study proposes a methodological framework to incorporate latent factors, including direct and indirect perceptions, as the explanatory variables in a discrete choice models using revealed preference and stated preference data sets. The methodology requires the estimation of a model system comprising of a discrete choice model and the structural and measurement equations of a latent variable model. The application involves the evaluation of responses to the new high occupancy vehicle (HOV) lanes on the Sun Yat‐Sen Freeway in Taiwan. The results obtained from this study provide valuable insights into the planning and assessment of HOV lanes.     

Automatic generation of the non-holonomic equations of motion for vehicle stability analysis

The mathematical analysis of vehicle stability has been utilised as an important tool in the design, development, and evaluation of vehicle architectures and stability controls. This paper presents a novel method for automatic generation of the linearised equations of motion for mechanical systems that is well suited to vehicle stability analysis. Unlike conventional methods for generating linearised equations of motion in standard linear second order form, the proposed method allows for the analysis of systems with non-holonomic constraints. In the proposed method, the algebraic constraint equations are eliminated after linearisation and reduction to first order. The described method has been successfully applied to an assortment of classic dynamic problems of varying complexity including the classic rolling coin, the planar truck–trailer, and the bicycle, as well as in more recent problems such as a rotor–stator and a benchmark road vehicle with suspension. This method has also been applied in the design and analysis of a novel three-wheeled narrow tilting vehicle with zero roll-stiffness. An application for determining passively stable configurations using the proposed method together with a genetic search algorithm is detailed. The proposed method and software implementation has been shown to be robust and provides invaluable conceptual insight into the stability of vehicles and mechanical systems.     

非自治随机微分方程的均方伪概周期温和解

主要考虑Hilbert空间上非自治随机微分方程均方伪概周期解存在的唯一性.利用不动点定理并结合发展系统理论,给出了这类非自治随机微分方程均方伪概周期解唯一存在的充分条件.